As onomatomaniak said, a person who habitually spreads rumors or engages in indiscreet talk (ie. gossips) can be referred to as a gossip. One thing to note, this would be independent of whether the things he or she tells are true or not.

Alternatively, you could also describe such a person as a rumourmonger, or even a scandalmonger, depending on the nature of the gossip and the intent.

One might call such a person a quidnunc, although that might be thought somewhat out-of-date nowadays. Merriam-Webster suggests quidnunc is more likely to be someone keen on hearing the latest gossip than repeating it, but I have never met anyone who just listened to scandal and rumour without passing it on.

Taleteller: One who tells tales or stories, especially in a mischievous or officious manner; a talebearer; a telltale; a tattler.

Slanderer: One who makes false and injurious statements about another, one who slanders, one who defames, one who maligns.

Backbiter: One who slanders, calumniates, or speaks ill of the absent; person who says nasty things about another person behind the
second person's back: that is, out of sight and hearing of the second
person.

I'm in the UK, and I don't think I've ever heard He is a blab. But this NGram strongly suggests this is primarily British usage. Blabbermouth, which sounds completely normal to me, appears to be the dominant American form.
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FumbleFingersDec 28 '11 at 16:31

Well I guess you are right mate, I am just an ordinary not native who has found the word in the dictionary :D I will try to remember blabbermouth - it sounds interesting. Cool nickname, mate.
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speedyGonzalesDec 29 '11 at 7:14

What is the single word that describes a person who always gossips? (For example, telling things about others which are not true.)

Tattle tail: One who tattles (reports others' wrongdoings), often by a child seeking attention.

ps: you did say that the person always gossips, whether they are true or not. the fact that they do it a lot could mean that the person thrives on it, suggests that it can be a child-like behavior seeking attention.

The correct spelling is tattletale, or tattle-tale, it's an easy one to get wrong, I had to think a bit before I realized. Good suggestion, though. Could you edit your answer, and perhpas include the link which you appeared to have quoted from: en.wiktionary.org/wiki/tattletale. Thanks!
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Mari-Lou ANov 14 '14 at 3:23

Please note that both gossip and gossiper are both given in the highest voted answer. You might do better to remove those and edit your answer to include an example of how to use blab and blabber
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Matt E. Эллен♦Jun 25 '14 at 10:11